Transcript The Photoelectric Effect

The Photoelectric Effect
Einstein’s Triumph
Graphics courtesy of Physics 2000, University of Colorado
Quantum Theory – Early
Experiments
• Cathode rays discovered in late 19th century
End of tube near +
terminal(anode) glowed
• Charge to mass ratio
e/m measured = E/B2r
evB = mv2/r
eE = evB etc
“Discovery” of Electron
• Cathode rays became known as electrons
• Most believed they were atoms
• J.J. Thompson believed they were parts of
atoms
• Millikin measured charge on electron
Millikin Oil Drop Experiment
• Shows that electron
charge is quantized.
• qe= integer x 1.6 x
10-19 C
Closer Look at Millikan Oil Drop
Millikan put a charge on a tiny
drop of oil and measured how
strong an applied electric field
had to be in order to stop the
oil drop from falling.
Planck Distribution
Wavelength distribution of
“blackbody” radiation
Planck E = hf
• Planck postulated that the radiators or
oscillators can only emit electromagnetic
radiation in finite amounts of energy.
• At a given temperature T, there is then not
enough thermal energy available to create
and emit many large radiation quanta. More
large energy quanta can be emitted,
however, when the temperature is raised.
Do You Know How a Solar Cell
Works?
Light produces electricity, right?
How?
The Photoelectric Effect, first explained
correctly by Einstein in 1905
Basic Info
• When light of high enough frequency
strikes a metal, electrons are given off
Apparatus
Simulations of Photoelectric
Effect
• Link #1
• Link #2
Planck’s E = hf
• Called quantum hypothesis
• Needed to explain spectrum of light given off by
hot objects
• Main idea: energy of atomic oscillators is not
continuous but finite number of discrete amounts
each related to frequency of oscillation by E =nhf
• h = 6.63 x 10-34 J-s (Planck’s Constant)
• Photons act like particles
Photoelectric Effect Apparatus
• When light hits cathode(-) current flows
• Electrons move toward anode (+)
o
Light
• If battery is reversed, electrons can be stopped
• KEmax = eV0 V0 is stopping voltage
What Wave Theory Predicts
• If light made brighter
– #electrons increases
– Maximum KE
increases
• If change frequency,
no effect on KE of
electrons
WRONG!
• Sorry Maxwell
What Photon Theory Predicts
• Increasing brightness
means more photons, not
more energy per photon
• Increasing frequency
increases KEmax (E=hf)
• Decreasing frequency
below “cutoff” could
mean no electrons ejected
Two Theories Animated
• Link
Now for the Math…
• Let hf be incoming energy of the photon
• Let W0 be the minimum energy required to
eject out through the surface(work function)
• KEmax is the maximum energy of the ejected
electron
• then hf = KEmax + W0
by conservation of energy in a collision
How to Analyze
• KEmax can be easily determined by
measuring the stopping potential
• KEmax =eV0 ( =qeV)
• So let’s plot KEmax vs. f
What Happens When Light
Frequency Increases?
• KEmax = hf - W0
f0 is called
threshold
frequency
KEmax
h is the slope
W0
f0
f
Meaning of Threshold(Cutoff)
Frequency
•
•
•
•
When f is less than f0 KEmax is negative.
There can be no photocurrent
The bigger f, the bigger is KEmax
At cutoff frequency f0 hf0 = W0
Problems
1. What stopping voltage is required to stop
an electron with KE of 1electron volt?
Ans. 1 volt
2. A stopping voltage of 2.5 volts is just
enough to stop all photocurrent. What is
KEmax?
Ans. 2.5 eV
Finding Photon Energy
• What is the energy of a photon of blue light
with l = 450 nm ?
HINT: First find f
f = c/l
E = hf = hc/l =
hc/l = (6.63x10-34 J-s)(3.0x108m/s)/(4.5 x 10-7 m)
= 4.42x10-19 J
/(1.6)x10-19 J/eV = 2.76 eV
Finding KEmax
• What is the maximum kinetic energy of
electrons ejected from a sodium surface
whose work function is W0 = 2.28 eV when
illuminated by light of wavelength 410nm?
hf = hc/l = 4.85x10-19 J
or 3.03 eV
(1243/410)
KEmax = hf - W0 = 3.03 eV – 2.28 eV = 0.75 eV
Finding Cutoff Frequency or
h =6.63 x 10 J-s
W = 2.28 eV
Wavelength
-34
0
• What is the cutoff frequency for sodium?
hf0 = W0 = 2.28 eV = 3.65 x 10-19 J
f0 = 3.65 x 10-19 J / 6.63 x 10-34 J-s = 5.5 x 1014 Hz
• What is the longest wavelength for a photo
current to flow?
l0 = c/f0 = 3.0 x 108 m/s /5.5 x 1014 Hz = 545 nm
Shortcut-click
Using 1243 Rule
• The wavelength corresponding to the work
function is just 1243/2.28 eV = 545 nm
How Can We Measure h Using
the Photoelectric Effect?
• Plot KEmax as a function of frequency
• h is the slope
• KEmax = hf - W0